A Pesquisa Operacional

[pic 1]

Nome: Rafael Andrade e Silva Mat.: 2102130030 X1 = Arredondamento X2 = Pecuária X3 = Soja

Max Z = 300x1 + 500x2 + 490x3		Z - 300x1 - 500x2 - 490x3 = 0
x1+x2+x3 <= 200 100x2 + 200x3 <= 23000 Sujeito a        1000000x2 + 2000000x3 <= 32750000 x1<=50 x1,x2,x3 >=0	-	x1 + x2 + x3 + xf1 = 200 100x2 + 200x3 + xf2 = 2300 Sujeito a        100000x2 + 200000x3 + xf3 = 327500 x1 + xf4 = 50

Função objetiva auxiliar

W = a4 + a5

a4 = -3x1 - 2x2 - 4x3 + xf4 + 210

a5 = -x1 + xf5 + 5

W = -4x1 - 2x2 - 4x3 + xf4 + xf5 = -215

Max: -W - 4x1 - 2x2 - 4x3 + xf4 + xf5 = -215

- Z -36x1 -45x2 -39x3

- X1 + X2 + X3 + Xf1 = 100

- 2x1 + x2 + xf2 = 210

- 4x1 + 3x2 + x3 + xf3 = 420

- 3x1 + 2x2 + 4x3 - xf4 + a4 = 210

→ x        x        x x        a

→ x1 - xf5 + a5 = 5

→ x2 + xf6 = 8

→x3 + xf7 = 90

→ -w - 4x1 - 2x2 + xf4 + xf5 = -215

Simplex:

Z	x1	x2	x3	xf1	xf2	xf3	xf4	b
1	-300	-500	-490	0	0	0	0	0
0	1	1	1	1	0	0	0	200
0	0	100	200	0	1	0	0	23000
0	0	100000	200000	0	0	1	0	32750000
0	1	0	0	0	0	0	1	50

0	1	1	1	1	0	0	0	200
0	1	1	1	1	0	0	0	200

[pic 2]

Z	x1	x2	x3	xf1	xf2	xf3	xf4	b
1	200	0	10	500	0	0	0	1000000
0	1	1	1	1	0	0	0	200
0	-100	0	100	-100	1	0	0	300
0	-1000000	0	1000000	-1000000	0	1	0	12750000
0	1	0	0	0	0	0	1	50

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